LINES AND ANGLES
FUNDAMENTALS
- Line Segment:- A part of line with two end points is called a line segment.
Here, line segment is denoted by \[\overline{AB}\].
- Ray;- A part of a line with one end point is called ray.
- Angle:- An angle is the union of two rays with a common initial point. It is denoted by \[\angle \].
The angle formed by two rays OX and OY is \[\angle XOY\] and \[\angle YOX.\]
- Acute angle:- Greater than \[{{0}^{{}^\circ }}\] but less than\[{{90}^{{}^\circ }}\].
Here, \[\theta \] is an obtuse angle.
- Obtuse angle:- Greater than 90° but less than \[{{180}^{{}^\circ }}\]
Here, \[\theta \] is a straight angle.
- Right angle:- Equal to \[{{90}^{{}^\circ }}\]
Here, \[\theta \] is a right angle.
- Straight angle:- Exactly equal to \[{{180}^{{}^\circ }}\]
Here, \[\theta \] is an acute angle.
- Reflex angle:- Greater then \[{{180}^{{}^\circ }}\] but less then \[{{360}^{{}^\circ }}\]
Here, \[\theta \] is reflex angle
- Complementary angle:- Two angles whose sum is \[90{}^\circ \] are called complementary angles.
\[\angle XOZ\] and \[\angle YOZ\] are complementary angles.
- Supplementary angle:- Two angles whose sum is \[180{}^\circ \] are called supplementary angles.
\[\angle XOZ\] and \[\angle YOZ\] are supplementary angles.
- Adjacent angle:- Two angles are said to be adjacent angle if they have the same vertex and a common arm and uncommon arm on the either side of the common arm.
\[\angle 1\] and \[\angle 2\]are called Adjacent angles.
- Linear pair of angles:- Two adjacent angles are called linear pair of angles if their non- common arms are two opposite rays. These angles are supplementary.
Angle \[\angle 1\] and \[\angle 2\] are linear pair of angles.
- Vertically opposite angle:- Two angles are called vertically opposite angles if their arms form two pairs of opposite rays. These two vertically opposite angles are equal.
\[\angle 1\] and \[\angle 3\] are vertically opposite angles and also \[\angle 2\] and \[\angle 4\] are vertically opposite angles.
- Corresponding angles:- \[\angle 1=\angle 5,\angle 2=\angle 6\]
\[\angle 3-\angle 7,\text{ }\angle 4=\angle 8\]
- Alternate interior angles:- \[\angle 3=\angle 6\text{ and }\angle 4=\angle 5\]
- Co - interior angles:- \[\angle 3\] and \[\angle 5,\angle 4\] and \[\angle 6\] and their sum is equal to \[{{180}^{{}^\circ }}\]
- Vertically opposite angles:- \[\angle \text{1}=\angle 4,\angle 2=\angle 3,\angle 5=\angle 8,\text{ }\angle 6=\angle 7\]
